Some Effects of Different Constitutive Laws on FSI Simulation for the Mitral Valve

Multi-Modal in Vitro Experiments Mimicking the Flow Through a Mitral Heart Valve Phantom

PURPOSE

Fluid-structure interaction (FSI) models are more commonly applied in medical research as computational power is increasing. However, understanding the accuracy of FSI models is crucial, especially in the context of heart valve disease in patient-specific models. Therefore, this study aimed to create a multi-modal benchmarking data set for cardiac-inspired FSI models, based on clinically important parameters, such as the pressure, velocity, and valve opening, with an in vitro phantom setup.

METHOD

An in vitro setup was developed with a 3D-printed phantom mimicking the left heart, including a deforming mitral valve. A range of pulsatile flows were created with a computer-controlled motor-and-pump setup. Catheter pressure measurements, magnetic resonance imaging (MRI), and echocardiography (Echo) imaging were used to measure pressure and velocity in the domain. Furthermore, the valve opening was quantified based on cine MRI and Echo images.

RESULT

The experimental setup, with 0.5% cycle-to-cycle variation, was successfully built and six different flow cases were investigated. Higher velocity through the mitral valve was observed for increased cardiac output. The pressure difference across the valve also followed this trend. The flow in the phantom was qualitatively assessed by the velocity profile in the ventricle and by streamlines obtained from 4D phase-contrast MRI.

CONCLUSION

A multi-modal set of data for validation of FSI models has been created, based on parameters relevant for diagnosis of heart valve disease. All data is publicly available for future development of computational heart valve models.

Validation of fluid-structure interaction simulations of the opening phase of phantom mitral heart valves under physiologically inspired conditions

BACKGROUND AND OBJECTIVE

Atrioventricular valve disease is a common cause of heart failure, and successful surgical or interventional outcomes are crucial. Patient-specific fluid-structure interaction (FSI) modeling may provide valuable insights into valve dynamics and guidance of valve repair strategies. However, lack of validation has kept FSI modeling from clinical implementation. Therefore, this study aims to validate FSI simulations against in vitro benchmarking data, based on clinically relevant parameters for evaluating heart valve disease.

METHODS

An FSI model that mimics the left heart was developed. The domain included a deformable mitral valve of different stiffnesses run with different inlet velocities. Five different cases were simulated and compared to in vitro data based on the pressure difference across the valve, the valve opening, and the velocity in the flow domain.

RESULTS

The simulations underestimate the pressure difference across the valve by 6.8-14 % compared to catheter measurements. Evaluation of the valve opening showed an underprediction of 5.4-7.3 % when compared to cine MRI, 2D Echo, and 3D Echo data. Additionally, the simulated velocity through the valve showed a 7.9-8.4 % underprediction in relation to Doppler Echo measurements. Qualitative assessment of the velocity profile in the ventricle and the streamlines of the flow in the domain showed good agreement of the flow behavior.

CONCLUSIONS

Parameters relevant to the diagnosis of heart valve disease estimated by FSI simulations showed good agreement when compared to in vitro benchmarking data, with differences small enough not to affect the grading of heart valve disease. The FSI model is thus deemed good enough for further development toward patient-specific cases.

Fluid-structure interaction and structural simulation of high acceleration effects on surgical repaired human mitral valve biomechanics

Mitral valve dynamics depend on force stability in the mitral leaflets, the mitral annulus, the chordae tendineae, and the papillary muscles. In chordal rupture conditions, the proper function of the valve disrupts, causing mitral regurgitation, the most prevalent valvular disease. In this study, Structural and FSI frameworks were employed to study valve dynamics in healthy, pathologic, and repaired states. Anisotropic, non-linear, hyper-elastic material properties applied to tissues of the valve while the first-order Ogden model reflected the best compatibility with the empirical data. Hemodynamic blood pressure of the cardiovascular system is applied on the leaflets as uniform loads varying by time, and exposure to high acceleration loads imposed on models. Immersed boundary method used for simulation of fluid in a cardiac cycle. In comparison between healthy and pathologic models, stress values and chordal tensions are increased, by nearly threefold and twofold, respectively. Stress concentration on leaflets is reduced by 75% after performing a successful surgical repair on the pathological model. Crash acceleration loads led to more significant stress and chordae tension on models, by 27% and 23%, respectively. It is concluded that a more sophisticated model could lead to a better understanding of human heart valve biomechanics in various conditions. If a preoperative plan is developed based on these modeling methods, the requirement for multiple successive repairs would be eliminated, operative times are shortened, and patient outcomes are improved.

Fluid-structure interaction simulation of calcified aortic valve stenosis

Calcified aortic valve stenosis (CAVS) is caused by calcium buildup and tissue thickening that impede the blood flow from left ventricle (LV) to aorta. In recent years, CAVS has become one of the most common cardiovascular diseases. Therefore, it is necessary to study the mechanics of aortic valve (AV) caused by calcification. In this paper, based on a previous idealized AV model, the hybrid immersed boundary/finite element method (IB/FE) is used to study AV dynamics and hemodynamic performance under normal and calcified conditions. The computational CAVS model is realized by dividing the AV leaflets into a calcified region and a healthy region, and each is described by a specific constitutive equation. Our results show that calcification can significantly affect AV dynamics. For example, the elasticity and mobility of the leaflets decrease due to calcification, leading to a smaller opening area with a high forward jet flow across the valve. The calcified valve also experiences an increase in local stress and strain. The increased loading due to AV stenosis further leads to a significant increase in left ventricular energy loss and transvalvular pressure gradients. The model predicted hemodynamic parameters are in general consistent with the risk classification of AV stenosis in the clinic. Therefore, mathematical models of AV with calcification have the potential to deepen our understanding of AV stenosis-induced ventricular dysfunction and facilitate the development of computational engineering-assisted medical diagnosis in AV related diseases.

Biomechanical characterization of the passive response of the thoracic aorta in chronic hypoxic newborn lambs using an evolutionary strategy

The present study involves experiments and modelling aimed at characterizing the passive structural mechanical behavior of the chronic hypoxic lamb thoracic aorta, whose gestation, birth and postnatal period were carried at high altitude (3600 masl). To this end, the mechanical response was studied via tensile and pressurization tests. The tensile and pressurization tests measurements were used simultaneously to calibrate the material parameters of the Gasser-Holzapfel-Ogden (GHO) hyperelasctic anisotropic constitutive model through an analytical-numerical optimization procedure solved with an evolutionary strategy that guarantees a stable response of the model. The model and procedure of calibration adequately adjust to the material behavior in a wide deformation range with an appropriate physical description. The results of this study predict the mechanical response of the lamb thoracic aorta under generalized loading states like those that can occur in physiological conditions and/or in systemic arterial hypertension. Finally, the novel use of the evolutionary strategy, together with the set of experiments and tools used in this study, provide a robust alternative to validate biomechanical characterizations.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid-Structure Interaction Simulation

Built on the hybrid immersed boundary/finite element (IB/FE) method, fluid-structure interaction (FSI) simulations of aortic valve (AV) dynamics are performed with three different constitutive laws and two different fiber architectures for the AV leaflets. An idealized AV model is used and mounted in a straight tube, and a three-element Windkessel model is further attached to the aorta. After obtaining ex vivo biaxial tensile testing of porcine AV leaflets, we first determine the constitutive parameters of the selected three constitutive laws by matching the analytical stretch-stress relations derived from constitutive laws to the experimentally measured data. Both the average error and relevant R-squared value reveal that the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions could be more suitable for characterizing the mechanical behaviors of the AV leaflets. We then thoroughly compare the simulation results from both structural mechanics and hemodynamics. Compared to the other two constitutive laws, the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions shows the larger leaflet displacements at the opened state, the largest forward jet flow, the smaller regurgitant flow. We further analyze hemodynamic parameters of the six different cases, including the regurgitant fraction, the mean transvalvular pressure gradient, the effective orifice area, and the energy loss of the left ventricle. We find that the fiber architecture with body-fitted orientation shows better dynamic behaviors in the leaflets, especially with the constitutive law using exponential terms for both the fiber and cross-fiber directions. In conclusion, both constitutive laws and fiber architectures can affect AV dynamics. Our results further suggest that the strain energy function with exponential terms for both the fiber and cross-fiber directions could be more suitable for describing the AV leaflet mechanical behaviors. Future experimental studies are needed to identify competent constitutive laws for the AV leaflets and their associated fiber orientations with controlled experiments. Although limitations exist in the present AV model, our results provide important information for selecting appropriate constitutive laws and fiber architectures when modeling AV dynamics.

An image-based computational hemodynamics study of the Systolic Anterior Motion of the mitral valve

Systolic Anterior Motion (SAM) of the mitral valve - often associated with Hypertrophic Obstructive Cardiomyopathy (HOCM) - is a cardiac pathology in which a functional subaortic stenosis is induced during systole by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of heart failure. In this paper, we propose a new computational pipeline, based on cardiac cine Magnetic Resonance Imaging (cine-MRI) data, for the assessment of SAM. The pipeline encompasses image processing of the left ventricle and the mitral valve, and numerical investigation of cardiac hemodynamics by means of Computational Fluid Dynamics (CFD) in a moving domain with image-based prescribed displacement. Patient-specific geometry and motion of the left ventricle are considered in view of an Arbitrary Lagrangian-Eulerian approach for CFD, while the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. We assess clinically relevant flow and pressure indicators in a parametric study for different degrees of SAM severity, in order to provide a better quantitative evaluation of the pathological condition. Moreover, we provide specific indications for its possible surgical treatment, i.e. septal myectomy.

Mathematical modeling and computer simulation of the three-dimensional pattern formation of honeycombs

We present a mathematical model, a numerical scheme, and computer simulations of the three-dimensional pattern formation of a honeycomb structure by using the immersed boundary method. In our model, we assume that initially the honeycomb cells have a hollow hemisphere mounted by a hollow circular cylinder shape at their birth and there is force acting upon the entire side of the cell. The net force from the individual cells is a key factor in their transformation from a hollow hemisphere mounted by a hollow circular cylinder shape to a rounded rhombohedral surfaces mounted by a hexagonal cylinder shape. Numerical simulations of the proposed mathematical model equation produce the rounded rhombohedral surfaces mounted by a hexagonal cylinder patterns observed in honeybee colonies.